Dynamic Event-Triggered Model Predictive Control With Guaranteed Rigorous Satisfaction of Probabilistic Path Constraints

Stochastic model predictive control (SMPC) with probabilistic path constraints remains an open and challenging issue due to the intractability of probabilistic path constraints, let alone guarantee rigorous satisfaction. For the SMPC problem, the greatest difficulty lies in how to solve a finite time domain optimal control problem in the corresponding sampling step while ensuring that the probabilistic path constraints are rigorously satisfied. Aiming at the above problem, this article presents a new method for SMPC with guaranteed rigorous satisfaction of probabilistic path constraints. Specifically, first, to convert thorny probabilistic path constraints into computationally solvable and equivalent deterministic constraints, a transformation technique is proposed by utilizing a designed ancillary feedback controller and the information on the probabilistic distribution of disturbances. Then, a probabilistic path-constrained dynamic event-triggered SMPC (DETSMPC) algorithm is further designed where not only control input can be obtained but also the probabilistic path constraints can be rigorously satisfied over the entire time domain. In addition, to mitigate redundant computation consumption, a novel event-triggering sampling scheme with two dynamic thresholds is proposed by the virtue of prediction horizon, real-time sampled data, and previous predicted and triggered states. Furthermore, it is proved that the proposed algorithm is feasible for the overall probabilistic path-constrained closed-loop DETSMPC system. Moreover, the convergence in probability of the closed-loop system is presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed methods.